TSTP Solution File: SET957+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET957+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:36:26 EDT 2023
% Result : Theorem 0.19s 0.58s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 53 ( 12 unt; 18 typ; 0 def)
% Number of atoms : 94 ( 21 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 97 ( 38 ~; 38 |; 15 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 10 >; 12 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-4 aty)
% Number of variables : 84 ( 4 sgn; 41 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_24,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_25,type,
singleton: $i > $i ).
tff(decl_26,type,
empty: $i > $o ).
tff(decl_27,type,
subset: ( $i * $i ) > $o ).
tff(decl_28,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk1_0: $i ).
tff(decl_30,type,
esk2_0: $i ).
tff(decl_31,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_32,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_33,type,
esk5_0: $i ).
tff(decl_34,type,
esk6_0: $i ).
tff(decl_35,type,
esk7_0: $i ).
tff(decl_36,type,
esk8_0: $i ).
tff(decl_37,type,
esk9_0: $i ).
tff(decl_38,type,
esk10_0: $i ).
tff(decl_39,type,
esk11_2: ( $i * $i ) > $i ).
fof(t110_zfmisc_1,conjecture,
! [X1,X2,X3,X4,X5,X6] :
( ( subset(X1,cartesian_product2(X2,X3))
& subset(X4,cartesian_product2(X5,X6))
& ! [X7,X8] :
( in(ordered_pair(X7,X8),X1)
<=> in(ordered_pair(X7,X8),X4) ) )
=> X1 = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t110_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(t103_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
~ ( subset(X1,cartesian_product2(X2,X3))
& in(X4,X1)
& ! [X5,X6] :
~ ( in(X5,X2)
& in(X6,X3)
& X4 = ordered_pair(X5,X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3,X4,X5,X6] :
( ( subset(X1,cartesian_product2(X2,X3))
& subset(X4,cartesian_product2(X5,X6))
& ! [X7,X8] :
( in(ordered_pair(X7,X8),X1)
<=> in(ordered_pair(X7,X8),X4) ) )
=> X1 = X4 ),
inference(assume_negation,[status(cth)],[t110_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
! [X32,X33] :
( subset(esk5_0,cartesian_product2(esk6_0,esk7_0))
& subset(esk8_0,cartesian_product2(esk9_0,esk10_0))
& ( ~ in(ordered_pair(X32,X33),esk5_0)
| in(ordered_pair(X32,X33),esk8_0) )
& ( ~ in(ordered_pair(X32,X33),esk8_0)
| in(ordered_pair(X32,X33),esk5_0) )
& esk5_0 != esk8_0 ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_7,plain,
! [X13,X14] : ordered_pair(X13,X14) = unordered_pair(unordered_pair(X13,X14),singleton(X13)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,plain,
! [X20,X21,X22,X23] :
( ( in(esk3_4(X20,X21,X22,X23),X21)
| ~ subset(X20,cartesian_product2(X21,X22))
| ~ in(X23,X20) )
& ( in(esk4_4(X20,X21,X22,X23),X22)
| ~ subset(X20,cartesian_product2(X21,X22))
| ~ in(X23,X20) )
& ( X23 = ordered_pair(esk3_4(X20,X21,X22,X23),esk4_4(X20,X21,X22,X23))
| ~ subset(X20,cartesian_product2(X21,X22))
| ~ in(X23,X20) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t103_zfmisc_1])])])]) ).
cnf(c_0_9,negated_conjecture,
( in(ordered_pair(X1,X2),esk5_0)
| ~ in(ordered_pair(X1,X2),esk8_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X11,X12] : unordered_pair(X11,X12) = unordered_pair(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,plain,
( X1 = ordered_pair(esk3_4(X2,X3,X4,X1),esk4_4(X2,X3,X4,X1))
| ~ subset(X2,cartesian_product2(X3,X4))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk5_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk8_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
cnf(c_0_14,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( X1 = unordered_pair(unordered_pair(esk3_4(X2,X3,X4,X1),esk4_4(X2,X3,X4,X1)),singleton(esk3_4(X2,X3,X4,X1)))
| ~ in(X1,X2)
| ~ subset(X2,cartesian_product2(X3,X4)) ),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk5_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk8_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( unordered_pair(singleton(esk3_4(X1,X2,X3,X4)),unordered_pair(esk3_4(X1,X2,X3,X4),esk4_4(X1,X2,X3,X4))) = X4
| ~ subset(X1,cartesian_product2(X2,X3))
| ~ in(X4,X1) ),
inference(rw,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( in(X1,esk5_0)
| ~ subset(X2,cartesian_product2(X3,X4))
| ~ in(X1,esk8_0)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,negated_conjecture,
subset(esk8_0,cartesian_product2(esk9_0,esk10_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_20,plain,
! [X34,X35] :
( ( ~ in(esk11_2(X34,X35),X34)
| ~ in(esk11_2(X34,X35),X35)
| X34 = X35 )
& ( in(esk11_2(X34,X35),X34)
| in(esk11_2(X34,X35),X35)
| X34 = X35 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
cnf(c_0_21,negated_conjecture,
( in(ordered_pair(X1,X2),esk8_0)
| ~ in(ordered_pair(X1,X2),esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
( in(X1,esk5_0)
| ~ in(X1,esk8_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( in(esk11_2(X1,X2),X1)
| in(esk11_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk8_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk5_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_10]),c_0_10]) ).
cnf(c_0_25,negated_conjecture,
( esk8_0 = X1
| in(esk11_2(esk8_0,X1),esk5_0)
| in(esk11_2(esk8_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
esk5_0 != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
( in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk8_0)
| ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),esk5_0) ),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_28,plain,
( X1 = X2
| ~ in(esk11_2(X1,X2),X1)
| ~ in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
in(esk11_2(esk8_0,esk5_0),esk5_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_25]),c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( in(X1,esk8_0)
| ~ subset(X2,cartesian_product2(X3,X4))
| ~ in(X1,esk5_0)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_31,negated_conjecture,
subset(esk5_0,cartesian_product2(esk6_0,esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_32,negated_conjecture,
~ in(esk11_2(esk8_0,esk5_0),esk8_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26]) ).
cnf(c_0_33,negated_conjecture,
( in(X1,esk8_0)
| ~ in(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET957+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.33 % Computer : n012.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Sat Aug 26 11:16:40 EDT 2023
% 0.15/0.33 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.58 % Version : CSE_E---1.5
% 0.19/0.58 % Problem : theBenchmark.p
% 0.19/0.58 % Proof found
% 0.19/0.58 % SZS status Theorem for theBenchmark.p
% 0.19/0.58 % SZS output start Proof
% See solution above
% 0.19/0.59 % Total time : 0.012000 s
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59 % Total time : 0.014000 s
%------------------------------------------------------------------------------